To calculate the probability of randomly choosing a gel pen first and then a fountain pen after replacing the gel pen, we can follow these steps:
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Total number of pens: There are 20 pens in total (4 fountain pens, 10 gel pens, and 6 ballpoint pens).
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Probability of choosing a gel pen: \[ P(\text{gel pen}) = \frac{\text{number of gel pens}}{\text{total number of pens}} = \frac{10}{20} = \frac{1}{2} \]
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Replace the gel pen: Since we replace the gel pen back into the drawer, the total number of pens remains 20.
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Probability of choosing a fountain pen: \[ P(\text{fountain pen}) = \frac{\text{number of fountain pens}}{\text{total number of pens}} = \frac{4}{20} = \frac{1}{5} \]
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Combined probability: Since these are independent events (choosing a gel pen and then a fountain pen), we multiply the probabilities: \[ P(\text{gel pen and then fountain pen}) = P(\text{gel pen}) \times P(\text{fountain pen}) = \frac{1}{2} \times \frac{1}{5} = \frac{1}{10} \]
Thus, the probability of randomly choosing a gel pen, replacing it, and then choosing a fountain pen is \(\frac{1}{10}\).
The correct answer is 1/10.